What is the crossover frequency to the Compression Driver in the Active Crossover?

Just guessing, but if for example the Active Crossover Frequency were ...say... 2khz and the lower limit of the Compression Driver were say 500hz, then I would add a capacitor at about 1khz. Since the Capacitor represent a High-PASS filter, using a capacitor below the Crossover Frequency will assure that all the wanted frequencies will get through.

Keep in mind that is just a guess on my part. I'm sure others will have better suggestions.

I think it depends on the frequency of the Pulse you are trying to block. If you can get an oscilloscope, ideally one with memory or capture, and you can determine the pulse width of the pulse when the amps shut off. They you will have some sense of the frequency you need to block.